The Obama administration has expressed concern at what US officials see as Britain's slide towards the European exit door.

Washington firmly believes that the departure of its strongest partner in Europe would also reduce American influence on the continent, as Britain so often shares American views.

An EU without Britain would be seen as weaker on free trade and less reliable on defence and foreign policy issues.

With David Cameron now saying a Britain out of Europe was now "imaginable", US agitation has reached a new high.

After observing the rise in popularity of Ukip and the rise of anti-European sentiment generally, the issue was raised by President Barack Obama in a video-conference call with the Prime Minister on Tuesday. It was raised during bilateral discussions between officials this week.

"It is important to state very clearly that a strong UK in a strong Europe is in America's national interest," said a senior US administration official. "We recognise national states but see the EU as a force multiplier."

The White House is perplexed by the view held by some Euro-sceptics that the so-called Special Relationship would be enhanced by a British exit, because it believes Britain would have more clout as a full partner of the European club.

It acknowledges that some countries, like Britain, matter more than others in the EU, dismissing the notion that Washington only wants one phone number to dial for Europe to make life easier.

Britain's free trade philosophy is regarded as vital in preventing the union from drifting towards protectionism, while since World War Two, successive British governments have been more assertive on a variety of foreign policy issues, and more in line with American thinking, than other major European nations.

"We understand that a Europe without the UK would be a weaker Europe," said a Whitehall source.

"We are getting more and more questions about this, particularly from the US and China. People want to know what it would mean.

"But at the moment we are focused on making Europe work better for us. We are on focusing on free trade, the single market and commerce. We are committed to making the EU more competitive."

With the eurozone still in danger of collapse, and momentum building on the continent for greater fiscal and political union, the Government has edged towards holding a referendum on EU membership.

Conservatives are increasingly envisaging a future where Britain's involvement withdraws from European institution and limits its connections to the single market and free trade.

Ukip, which supports withdrawal from the union Britain joined under a Conservative government in 1973, has enjoyed strong showings in recent by-elections and has overtaken the Lib Dems to poll at between seven and 14 per cent.

The coalition is already considering opting out of numerous common judicial and policing measures contained in the Lisbon Treaty, which enshrined closer European integration, most notably the European arrest warrant.

Adding to American apprehension about Europe is the eurozone's slide back into recession, which Hillary Clinton, the US Secretary of State, has attributed to "austerity policies taking effect".

"I want to urge European leaders to keep working to address the challenge of economic growth and jobs," she said.

Senior US officials believe that even if an immediate threat of collapse has passed, eurozone leaders have not resolved problems in manner that gives long-term comfort.

William Dartmouth MEP, Ukip's foreign affairs spokesman said: "There have been times in history when the US has been very pleased that Britain has remained independent of the continent, and we expect that to continue.

"It is not the job of the UK to make the work of US diplomats easier. It is our job to secure our own interests."